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<div class="fragment"><pre class="fragment"><a name="l00001"></a>00001 <span class="comment">#!/usr/bin/python</span>
<a name="l00002"></a>00002 <span class="comment"># -*- coding: utf-8 -*-</span>
<a name="l00003"></a>00003 
<a name="l00004"></a>00004 <span class="comment"># Copyright (c) 2011</span>
<a name="l00005"></a>00005 <span class="comment">#</span>
<a name="l00006"></a>00006 <span class="comment"># Permission is hereby granted, free of charge, to any person obtaining a</span>
<a name="l00007"></a>00007 <span class="comment"># copy of this software and associated documentation files (the &quot;Software&quot;),</span>
<a name="l00008"></a>00008 <span class="comment"># to deal in the Software without restriction, including without limitation</span>
<a name="l00009"></a>00009 <span class="comment"># the rights to use, copy, modify, merge, publish, distribute, sublicense,</span>
<a name="l00010"></a>00010 <span class="comment"># and/or sell copies of the Software, and to permit persons to whom the</span>
<a name="l00011"></a>00011 <span class="comment"># Software is furnished to do so, subject to the following conditions:</span>
<a name="l00012"></a>00012 <span class="comment">#</span>
<a name="l00013"></a>00013 <span class="comment"># The above copyright notice and this permission notice shall be included in</span>
<a name="l00014"></a>00014 <span class="comment"># all copies or substantial portions of the Software.</span>
<a name="l00015"></a>00015 <span class="comment">#</span>
<a name="l00016"></a>00016 <span class="comment"># THE SOFTWARE IS PROVIDED &quot;AS IS&quot;, WITHOUT WARRANTY OF ANY KIND, EXPRESS OR</span>
<a name="l00017"></a>00017 <span class="comment"># IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,</span>
<a name="l00018"></a>00018 <span class="comment"># FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE</span>
<a name="l00019"></a>00019 <span class="comment"># AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER</span>
<a name="l00020"></a>00020 <span class="comment"># LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,</span>
<a name="l00021"></a>00021 <span class="comment"># OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE</span>
<a name="l00022"></a>00022 <span class="comment"># SOFTWARE.</span>
<a name="l00023"></a>00023 <span class="comment">#</span>
<a name="l00024"></a>00024 <span class="comment"># Author: Jesus Carrero &lt;j.o.carrero@gmail.com&gt;</span>
<a name="l00025"></a>00025 <span class="comment"># Mountain View, CA</span>
<a name="l00026"></a>00026 <span class="comment">#</span>
<a name="l00027"></a>00027 
<a name="l00028"></a>00028 <span class="stringliteral">&quot;&quot;&quot; time stepper of dirichlet boundary value problem &quot;&quot;&quot;</span>
<a name="l00029"></a>00029 
<a name="l00030"></a>00030 <span class="keyword">from</span> scipy <span class="keyword">import</span> linspace, zeros, arange
<a name="l00031"></a>00031 <span class="keyword">from</span> scipy.sparse.construct <span class="keyword">import</span> spdiags
<a name="l00032"></a>00032 <span class="keyword">from</span> scipy.sparse.linalg <span class="keyword">import</span> spsolve <span class="keyword">as</span> spsolve
<a name="l00033"></a>00033 
<a name="l00034"></a>00034 <span class="keyword">from</span> TimeStepper <span class="keyword">import</span> TimeStepper
<a name="l00035"></a>00035 
<a name="l00036"></a>00036 <span class="keyword">import</span> time
<a name="l00037"></a>00037 <span class="keyword">import</span> logging
<a name="l00038"></a>00038 
<a name="l00039"></a>00039 
<a name="l00040"></a><a class="code" href="classsolvers_1_1DirichletTimeStepper_1_1DirichletTimeStepper.html">00040</a> <span class="keyword">class </span><a class="code" href="classsolvers_1_1DirichletTimeStepper_1_1DirichletTimeStepper.html">DirichletTimeStepper</a>(TimeStepper):
<a name="l00041"></a>00041     <span class="stringliteral">&quot;&quot;&quot; time stepper for general convection-diffusion-reaction equation.&quot;&quot;&quot;</span>
<a name="l00042"></a>00042 
<a name="l00043"></a>00043     __slots__ = [<span class="stringliteral">&#39;m_lbc&#39;</span>, <span class="stringliteral">&#39;m_rbc&#39;</span>, <span class="stringliteral">&#39;m_time_solu&#39;</span>, <span class="stringliteral">&#39;m_impl_mat&#39;</span>, <span class="stringliteral">&#39;m_expl_mat&#39;</span>]
<a name="l00044"></a>00044 
<a name="l00045"></a>00045 
<a name="l00046"></a><a class="code" href="classsolvers_1_1DirichletTimeStepper_1_1DirichletTimeStepper.html#ac2f5f8548e4ee3cf3ec1de3a1923b821">00046</a>     <span class="keyword">def </span><a class="code" href="classsolvers_1_1DirichletTimeStepper_1_1DirichletTimeStepper.html#ac2f5f8548e4ee3cf3ec1de3a1923b821">__init__</a>(self, method=&#39;cn&#39;):
<a name="l00047"></a>00047         <span class="stringliteral">&quot;&quot;&quot;instantiate object of type Dirichlet time stepper.&quot;&quot;&quot;</span>
<a name="l00048"></a>00048         TimeStepper.__init__(self, method)
<a name="l00049"></a>00049         (self.<a class="code" href="classsolvers_1_1DirichletTimeStepper_1_1DirichletTimeStepper.html#abac331e1a28d1fccebdc0e35f3a2b705">m_lbc</a>, self.<a class="code" href="classsolvers_1_1DirichletTimeStepper_1_1DirichletTimeStepper.html#a0141ff3770d61885a945c3a8c6d00754">m_rbc</a>) = (<span class="keywordtype">None</span>, <span class="keywordtype">None</span>)
<a name="l00050"></a>00050         (self.<a class="code" href="classsolvers_1_1DirichletTimeStepper_1_1DirichletTimeStepper.html#abe374b517067938faa5cf4a51969d388">m_time_solu</a>, self.<a class="code" href="classsolvers_1_1DirichletTimeStepper_1_1DirichletTimeStepper.html#a51024f3229e0d9409b718915efd7b5f4">m_impl_mat</a>, self.<a class="code" href="classsolvers_1_1DirichletTimeStepper_1_1DirichletTimeStepper.html#a580e6e217dc2952ee7f605ba80e35b8d">m_expl_mat</a>) = (<span class="keywordtype">None</span>,
<a name="l00051"></a>00051                 <span class="keywordtype">None</span>, <span class="keywordtype">None</span>)
<a name="l00052"></a>00052 
<a name="l00053"></a>00053     <span class="keyword">def </span>_solve_fwd(self, rhs):
<a name="l00054"></a>00054         <span class="stringliteral">&quot;&quot;&quot;solve implicit problem.&quot;&quot;&quot;</span>
<a name="l00055"></a>00055 
<a name="l00056"></a>00056         <span class="keywordflow">return</span> spsolve(self.<a class="code" href="classsolvers_1_1DirichletTimeStepper_1_1DirichletTimeStepper.html#a51024f3229e0d9409b718915efd7b5f4">m_impl_mat</a>, rhs)
<a name="l00057"></a>00057 
<a name="l00058"></a>00058     <span class="keyword">def </span>__theta_stepper(self, tmp_solu, mass_bd, stiff_bd, i):
<a name="l00059"></a>00059         <span class="stringliteral">&quot;&quot;&quot;step using theta method.&quot;&quot;&quot;</span>
<a name="l00060"></a>00060 
<a name="l00061"></a>00061         tmp_solu = self.<a class="code" href="classsolvers_1_1DirichletTimeStepper_1_1DirichletTimeStepper.html#a580e6e217dc2952ee7f605ba80e35b8d">m_expl_mat</a> * tmp_solu
<a name="l00062"></a>00062 
<a name="l00063"></a>00063         left_bd = self.<a class="code" href="classsolvers_1_1DirichletTimeStepper_1_1DirichletTimeStepper.html#abac331e1a28d1fccebdc0e35f3a2b705">m_lbc</a>
<a name="l00064"></a>00064         right_bd = self.<a class="code" href="classsolvers_1_1DirichletTimeStepper_1_1DirichletTimeStepper.html#a0141ff3770d61885a945c3a8c6d00754">m_rbc</a>
<a name="l00065"></a>00065         theta = self.get_theta()
<a name="l00066"></a>00066 
<a name="l00067"></a>00067         tmp_solu[0] += (left_bd[i - 1] - left_bd[i]) * mass_bd[0, 0] \
<a name="l00068"></a>00068             + (theta * left_bd[i - 1] + (1 - theta) * left_bd[i]) \
<a name="l00069"></a>00069             * stiff_bd[0, 0]
<a name="l00070"></a>00070         tmp_solu[-1] += (right_bd[i - 1] - right_bd[i]) * mass_bd[0, 1] \
<a name="l00071"></a>00071             + (theta * right_bd[i - 1] + (1 - theta) * right_bd[i]) \
<a name="l00072"></a>00072             * stiff_bd[0, 1]
<a name="l00073"></a>00073 
<a name="l00074"></a>00074         <span class="keywordflow">if</span> 2 == mass_bd[:, 0].size:
<a name="l00075"></a>00075             tmp_solu[1] += (left_bd[i - 1] - left_bd[i]) * mass_bd[1,
<a name="l00076"></a>00076                     0] + (theta * left_bd[i - 1] + (1 - theta)
<a name="l00077"></a>00077                           * left_bd[i]) * stiff_bd[1, 0]
<a name="l00078"></a>00078             tmp_solu[-2] += (right_bd[i - 1] - right_bd[i]) \
<a name="l00079"></a>00079                 * mass_bd[1, 1] + (theta * right_bd[i - 1] + (1
<a name="l00080"></a>00080                                    - theta) * right_bd[i]) \
<a name="l00081"></a>00081                 * stiff_bd[1, 1]
<a name="l00082"></a>00082 
<a name="l00083"></a>00083         <span class="keywordflow">return</span> self.<a class="code" href="classsolvers_1_1DirichletTimeStepper_1_1DirichletTimeStepper.html#a63205a5de6930a8428c7ffcee530519f">_solve_fwd</a>(tmp_solu)
<a name="l00084"></a>00084 
<a name="l00085"></a>00085     <span class="keyword">def </span>_init_engine(self):
<a name="l00086"></a>00086         <span class="stringliteral">&quot;&quot;&quot;virtual method.&quot;&quot;&quot;</span>
<a name="l00087"></a>00087 
<a name="l00088"></a>00088         <span class="keywordflow">pass</span>
<a name="l00089"></a>00089 
<a name="l00090"></a>00090     <span class="keyword">def </span>__set_up_problem(self):
<a name="l00091"></a>00091         <span class="stringliteral">&quot;&quot;&quot;set up time marching scheme.&quot;&quot;&quot;</span>
<a name="l00092"></a>00092 
<a name="l00093"></a>00093         <span class="comment"># bwd, fwd matrices.</span>
<a name="l00094"></a>00094 
<a name="l00095"></a>00095         init_solu = self.get_initial_state()
<a name="l00096"></a>00096         solu_size = init_solu.size
<a name="l00097"></a>00097         delta_t = (self.get_expiry() - self.get_start_time()) \
<a name="l00098"></a>00098             / self.get_nsteps()
<a name="l00099"></a>00099         theta = self.get_theta()
<a name="l00100"></a>00100 
<a name="l00101"></a>00101         mdiags = self.get_mass_matrix()
<a name="l00102"></a>00102         sdiags = self.get_stiffness_matrix()
<a name="l00103"></a>00103         dposi = self.get_diag_posi()
<a name="l00104"></a>00104 
<a name="l00105"></a>00105         fwd_diag_mat = mdiags - (1.0 - theta) * delta_t \
<a name="l00106"></a>00106             * sdiags
<a name="l00107"></a>00107         bwd_diag_mat = mdiags + theta * delta_t * sdiags
<a name="l00108"></a>00108         self.m_impl_mat = spdiags(fwd_diag_mat, dposi, solu_size,
<a name="l00109"></a>00109                                   solu_size, format=<span class="stringliteral">&#39;csr&#39;</span>)
<a name="l00110"></a>00110         self.m_expl_mat = spdiags(bwd_diag_mat, dposi, solu_size,
<a name="l00111"></a>00111                                   solu_size, format=<span class="stringliteral">&#39;csr&#39;</span>)
<a name="l00112"></a>00112 
<a name="l00113"></a>00113         self._init_engine()
<a name="l00114"></a>00114 
<a name="l00115"></a>00115         <span class="comment"># boundary conditions in time</span>
<a name="l00116"></a>00116 
<a name="l00117"></a>00117         dtime = linspace(self.get_start_time(), self.get_expiry(),
<a name="l00118"></a>00118                          self.get_nsteps() + 1, <span class="stringliteral">&#39;True&#39;</span>)
<a name="l00119"></a>00119 
<a name="l00120"></a>00120         (left_point, right_point) = self.get_left_right()
<a name="l00121"></a>00121         self.m_lbc = self.eval_left_bc(left_point, dtime)
<a name="l00122"></a>00122         self.m_rbc = self.eval_right_bd_cond(right_point,
<a name="l00123"></a>00123                 dtime)
<a name="l00124"></a>00124 
<a name="l00125"></a>00125         <span class="keywordflow">if</span> self.keep_history():
<a name="l00126"></a>00126             self.m_time_solu = zeros((self.m_lbc.size, init_solu.size
<a name="l00127"></a>00127                     + 2), <span class="stringliteral">&#39;float64&#39;</span>)
<a name="l00128"></a>00128             self.m_time_solu[0, 1:-1] = init_solu.flatten()
<a name="l00129"></a>00129             self.m_time_solu[:, 0] = self.m_lbc.flatten()
<a name="l00130"></a>00130             self.m_time_solu[:, -1] = self.m_rbc.flatten()
<a name="l00131"></a>00131 
<a name="l00132"></a>00132         <span class="keywordflow">return</span> delta_t
<a name="l00133"></a>00133 
<a name="l00134"></a><a class="code" href="classsolvers_1_1DirichletTimeStepper_1_1DirichletTimeStepper.html#a0b2db05b35771fd3e3bc45039f18ea78">00134</a>     <span class="keyword">def </span><a class="code" href="classsolvers_1_1DirichletTimeStepper_1_1DirichletTimeStepper.html#a0b2db05b35771fd3e3bc45039f18ea78">get_history</a>(self):
<a name="l00135"></a>00135         <span class="stringliteral">&quot;&quot;&quot; get solution at each time step. &quot;&quot;&quot;</span>
<a name="l00136"></a>00136 
<a name="l00137"></a>00137         <span class="keywordflow">return</span> self.<a class="code" href="classsolvers_1_1DirichletTimeStepper_1_1DirichletTimeStepper.html#abe374b517067938faa5cf4a51969d388">m_time_solu</a>
<a name="l00138"></a>00138 
<a name="l00139"></a><a class="code" href="classsolvers_1_1DirichletTimeStepper_1_1DirichletTimeStepper.html#acfaa8905a5d4889edd2670474b47760d">00139</a>     <span class="keyword">def </span><a class="code" href="classsolvers_1_1DirichletTimeStepper_1_1DirichletTimeStepper.html#acfaa8905a5d4889edd2670474b47760d">get_impl_mat</a>(self):
<a name="l00140"></a>00140         <span class="stringliteral">&quot;&quot;&quot; return matix for impl step. &quot;&quot;&quot;</span>
<a name="l00141"></a>00141 
<a name="l00142"></a>00142         <span class="keywordflow">return</span> self.<a class="code" href="classsolvers_1_1DirichletTimeStepper_1_1DirichletTimeStepper.html#a51024f3229e0d9409b718915efd7b5f4">m_impl_mat</a>
<a name="l00143"></a>00143 
<a name="l00144"></a><a class="code" href="classsolvers_1_1DirichletTimeStepper_1_1DirichletTimeStepper.html#a230879ff23d5cee49c4df6d28bc01424">00144</a>     <span class="keyword">def </span><a class="code" href="classsolvers_1_1DirichletTimeStepper_1_1DirichletTimeStepper.html#a230879ff23d5cee49c4df6d28bc01424">step</a>(self):
<a name="l00145"></a>00145         <span class="stringliteral">&quot;&quot;&quot; march in time. ( solve the bvp )&quot;&quot;&quot;</span>
<a name="l00146"></a>00146 
<a name="l00147"></a>00147         delta_t = self.<a class="code" href="classsolvers_1_1DirichletTimeStepper_1_1DirichletTimeStepper.html#a009bb4573fa923f3ee82e030944c4bec">__set_up_problem</a>()
<a name="l00148"></a>00148 
<a name="l00149"></a>00149         start = time.time()
<a name="l00150"></a>00150         tmp_solu = self.get_initial_state().copy()
<a name="l00151"></a>00151 
<a name="l00152"></a>00152         (mass_bd, stiff_bd) = self.get_mass_stiff_at_bd()
<a name="l00153"></a>00153         stiff_bd = delta_t * stiff_bd
<a name="l00154"></a>00154 
<a name="l00155"></a>00155         <span class="keywordflow">for</span> i <span class="keywordflow">in</span> arange(1, self.get_nsteps() + 1):
<a name="l00156"></a>00156             tmp_solu = self.<a class="code" href="classsolvers_1_1DirichletTimeStepper_1_1DirichletTimeStepper.html#a485c9112af97860ed5124c11e3a62d1e">__theta_stepper</a>(tmp_solu, mass_bd,
<a name="l00157"></a>00157                     stiff_bd, i)
<a name="l00158"></a>00158             <span class="keywordflow">if</span> self.keep_history():
<a name="l00159"></a>00159                 self.<a class="code" href="classsolvers_1_1DirichletTimeStepper_1_1DirichletTimeStepper.html#abe374b517067938faa5cf4a51969d388">m_time_solu</a>[i, 1:-1] = tmp_solu.flatten()
<a name="l00160"></a>00160 
<a name="l00161"></a>00161         <span class="keywordflow">if</span> self.time_stepper_log():
<a name="l00162"></a>00162             log_progress = logging.getLogger(<span class="stringliteral">&#39;log_progress&#39;</span>)
<a name="l00163"></a>00163             log_progress.info(<span class="stringliteral">&#39;Time Stepping     takes &#39;</span>
<a name="l00164"></a>00164                               + str(time.time() - start) + <span class="stringliteral">&#39; secs&#39;</span>)
<a name="l00165"></a>00165 
<a name="l00166"></a>00166         solution = zeros((tmp_solu.size + 2, 1))
<a name="l00167"></a>00167         solution[1:-1, 0] = tmp_solu.flatten()
<a name="l00168"></a>00168         solution[0, 0] = self.<a class="code" href="classsolvers_1_1DirichletTimeStepper_1_1DirichletTimeStepper.html#abac331e1a28d1fccebdc0e35f3a2b705">m_lbc</a>[-1]
<a name="l00169"></a>00169         solution[-1, 0] = self.<a class="code" href="classsolvers_1_1DirichletTimeStepper_1_1DirichletTimeStepper.html#a0141ff3770d61885a945c3a8c6d00754">m_rbc</a>[-1]
<a name="l00170"></a>00170         <span class="keywordflow">return</span> solution
<a name="l00171"></a>00171 
<a name="l00172"></a>00172 
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